* Big blast hits Afghan capital during morning rush hour
* Taliban claim responsibility for suicide car bomb attack
* Police say at least 28 dead, hundreds wounded
* First attack in Kabul since Taliban's "spring offensive" began
A major Taliban suicide bomb and gun attack on a government security office in central Kabul during rush hour on Tuesday killed at least 28 people and wounded more than 320, a week after the militant group announced a spring offensive.
President Ashraf Ghani condemned the assault "in the strongest possible terms" in a statement from the presidential palace, only a few hundred metres away from the scene of the blast in the Afghan capital.
The insurgency led by the Afghan Taliban has gained strength since the withdrawal of most international combat troops at the end of 2014, and the Islamist group is believed to be stronger than at any point since it was driven from power by U.S.-backed local forces in 2001.
Police chief Abdul Rahman Rahimi said civilians and members of the Afghan security forces were among the dead and wounded.
The brazen attack began with a suicide car bomb and security forces and militants then exchanged gunfire, Reuters witnesses near the scene said.
The Taliban said on their Pashto-language website that they had carried out the suicide bombing on "Department 10", an NDS (National Directorate of Security) unit which is responsible for protecting government ministers and VIPs.
They said a suicide car bomber blew up the main gate at the front of the office, allowing other fighters, including more suicide bombers, to enter the heavily guarded compound.
Taliban spokesman Zabihullah Mujahid said in a separate statement that the attackers were engaged in a gunbattle with Afghan security forces inside the building.
It was not immediately possible to verify the details of the Taliban's claim with government officials. The Islamist group often exaggerates details of attacks against government and military targets.
A thick plume of black smoke was seen rising from the area near the sprawling U.S. embassy complex immediately after the blast.
Warning sirens blared out for some minutes from the embassy compound, which is also close to the headquarters of the NATO-led Resolute Support mission.
The U.S. embassy and the NATO mission both said they were not affected by the blast.
The Taliban announced the beginning of their spring offensive on April 12, and fighting has raged around the symbolically important northern city of Kunduz since then, although the capital had been relatively quiet.
Kunduz, Afghanistan's fifth-largest city, fell briefly to the Taliban last September in the biggest blow to Ghani's government since NATO-led forces ended their combat operations at the end of 2014.
Tuesday's blast came days after a United Nations report said urban warfare had caused a spike in the number of deaths and injuries among women and children in Afghanistan this year as the Taliban intensify their campaign against Ghani's Western-backed government.